Many different types of commercial pepper mills are disclosed in, for example, Taiwan Pat. No. 416,299, U.S. Pat. Nos. 6,443,377, 6,443,378, and 6,830,205. The gear sets of these conventional pepper mills are composed of cone-shaped grinding blocks and grinding rings attached thereon, wherein the peppercorns are ground by the engagement motion between the respective protrudent gears of the cone-shaped grinding blocks and grinding rings. The above-mentioned engagement motion is performed only along arc-shaped tracks in a unitary direction since no reverse thread is formed on the cone-shaped grinding blocks and the grinding rings. In other words, if the conventional grinding blocks of the conventional pepper mills are rotated reversely, the grinding blocks cannot engage with the grinding rings. Therefore, the idle grinding blocks may be damaged easily by the friction between the grinding rings and the grinding blocks.